Combinatorics

  1. Graph Theory and Combinatorics
    1. Basic Graph Enumeration
      1. Counting Labeled Graphs
        1. Counting Unlabeled Graphs
          1. Polya Enumeration Theory
          2. Counting Trees
            1. Definition of Trees
              1. Cayley's Formula for Labeled Trees
                1. Prüfer Sequences
                  1. Bijection with Trees
                    1. Encoding and Decoding
                    2. Counting Unlabeled Trees
                      1. Rooted Trees
                        1. Binary Trees
                        2. Counting Spanning Trees
                          1. Definition of Spanning Trees
                            1. The Matrix Tree Theorem
                              1. Kirchhoff's Theorem
                                1. Applications in Network Theory
                                2. Graph Coloring
                                  1. Vertex Coloring
                                    1. Chromatic Number
                                      1. Chromatic Polynomials
                                        1. Definition and Properties
                                          1. Deletion-Contraction Formula
                                            1. Examples and Calculations
                                            2. Edge Coloring
                                              1. Applications of Graph Coloring
                                              2. Matchings and Coverings
                                                1. Perfect Matchings
                                                  1. Counting Matchings
                                                    1. Hall's Marriage Theorem
                                                      1. König's Theorem

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                                                    9. Special Counting Numbers and Sequences

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                                                    11. Design Theory